Calculation and analysis method of limit load, deformation and energy dissipating of ring net panel in flexible protection system

ABSTRACT

A calculation method of limit load, deformation and energy dissipating of a ring net panel of a flexible protection net, includes step (1): determining geometrical parameters of the ring net, connection type of steel rings, and diameter of steel wires; step (2): determining a loading rate, a loaded region and a boundary condition of the ring net panel; step (3): obtaining basic mechanical parameters of materials through tests, and establishing a critical damage criterion of the ring net panel; step (4): establishing an equivalent calculation model of a ring net panel based on a fiber-spring unit; and step (5): calculating a puncturing displacement, a puncturing load and energy dissipating of the ring net panel. The method adopts a calculation assumption of load path equivalence.

CROSS REFERENCES TO THE RELATED APPLICATIONS

This application is based upon and claims priority to Chinese PatentApplication No. 202010365241.1, filed on Apr. 30, 2020, the entirecontents of which are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a calculation and analysis method of aring net panel in a flexible protection system, belongs to the field ofside slope protection engineering, and more particularly, to acalculation method of limit load, deformation and energy dissipating ofthe ring net panel of a flexible protection net.

BACKGROUND

Recently, due to the comprehensive influence of human factors such as aman-made slope of road, excessive exploration, etc. and natural factorssuch as heavy rain, extreme rainfall, etc., geological disasters such ascollapse and rockfall, landslide, debris flow, etc. occur frequently insouthwest and southeast hilly mountainous regions and northwest regionsin China. These situations present significant hidden danger for causingdamage to property and person. The flexible protection system, a newinterception structure, is commonly applied to the field of geologicaldisaster protection.

The flexible protection system is a complex non-linear structure systemcomposed of a support part (steel column), an interception part(flexible net), an energy dissipating part (decompression ring), aconnection part (steel rope, shackle) and an anchor part (base, anchorpole). The flexible interception net is a key part of successfullyimplementing a safety protection function of the flexible protectionsystem. It bears the direct impact, for example, of falling rocks. Oncethe net is damaged, the protection system loses its loading andprotection function. At present, a rhombic net, a double twistedhexagonal net, a G.T.S net, a ring net and the like are often adopted asinterception parts in the flexible protection system.

Compared with other types of nets, the ring net panel has a greaterdeformation and load bearing ability, which are often applied to a highenergy level protection net. The ring net is formed by a looseconnection, and thus when the ring panel is subjected to the impact,non-linear characteristics such as strong contact, slippage, damage andthe like typically occur. As a result, the design of the flexibleprotection system has become very complex. Quantitative evaluation forthe deformation, loading and energy dissipating abilities is criticalfor designing the ring net so that its safety protection function isoptimal.

At present, the relevant standard with respect to engineering design ofthe flexible protection system includes only two industry standards,that is, “The flexible safety net for protection of slope along theline” (TB/T3089-2004) and “Component of flexible system for protectinghighway slope” (JT/T 528-2004) in China. In the two industry standards,products, such as the steel rope, shackle, decompression ring and thelike, are inspected by the inspection methods and requirements under astatic condition. However, the evaluation method is simple, and acomprehensive evaluation index with respect to safety performances suchas deformation, loading, energy dissipating and the like of the ring netpanel is not considered by the current method either. Therefore, it isdifficult to ensure a reasonable and competent selection and engineeringdesign for the interception part in the practical engineering. The netpanel is considered as a portion of the force transmission parts of thesystem, and a type and size of the ring net panel are designed accordingto the limited test result, which cannot perform quantitativecalculation for out-of-plane deformation, loading and energy dissipatingabilities of the ring net panel to formulate the basis of a reliabledesign.

The deformation ability of the ring net panel depends on a looseconnection and a non-linear deformation between net rings. These areimportant for guaranteeing formation of an optimal buffering ability ofthe flexible protection system. Compared with a rigid structure, largedeformation of the flexible net on impact significantly prolongs theduration time of impact. This effectively reduces the impact force peak,thereby reducing internal forces of other parts such as the steelcolumn, support rope and the like in the system reducing the degree ofdamage to the protection system. The loading ability of the ring netpanel depends on the material strength of a high-strength steel rope andthe number of winding turns of a net ring.

The loading ability is also influenced by factors such as the number ofstrands of the steel rope, an area of the loaded region, boundaryconstraint and the like. The loading ability of the ring panel is a keyindex indicating whether the interception function can be implemented.The energy dissipating ability of the ring net panel depends on a commonresult of the deformation ability and the loading ability, which ismatched with a protection level index of the flexible protection system,and adapted to a design method based on energy matching in the design ofthe protection system. The deformation, loading and energy dissipatingabilities of the ring net panel together form the comprehensiveevaluation index of the safety of the interception parts of theprotection system. In the practical engineering, a quantitative analysismethod of performance evaluation of the ring net panel is established toensure a reliable design of the protection net, which is significant toimprove the interception effect for geological disasters such asrockfalls, landslides, debris flows, etc. and reduce losses of thedisasters. Thus, an improved quantitative analysis method of performanceevaluation of the ring panel is highly desirable.

SUMMARY

The objective of the present invention is to provide a calculationmethod of limit load, deformation and energy dissipating of a ring netpanel of a flexible protection net that is capable of solving theexisting problem that the safety performance evaluation and the designselection of the interception net panel in the flexible protection netsystem lack a quantitative description method for guaranteeing that theinterception net panel of the protection net may achieve the protectionability required by its design.

The above purpose of the present invention is implemented through thefollowing technical solutions.

The calculation method of the limit load, deformation and energydissipating of the ring net panel of the flexible protection netincludes the following steps:

Step (1): determining geometrical parameters of the ring net panel, anested net ring and a wound steel rope.

The ring net panel is connected to a support part having a protectionstructure through a shackle and the steel rope, and is manufactured bynesting single rings, an inner diameter of the single ring is d. Eachsingle ring is manufactured by winding the steel rope having a diameterof d_(min), to form different numbers of turns n_(w), and across-sectional area of the single ring is A

$A = \frac{n_{w}\pi d_{\min}^{2}}{4}$

The ring net panel has a length w_(x) and a width w_(y), afour-nested-into-one ring net panel is formed by using a minimum steelrope having a total length of l_(wire)

${l_{wire} = {\frac{n_{w}\pi\; d}{2\sqrt{2}d}\lbrack {{( {w_{x} - d + {2\sqrt{2}d}} )\;( {w_{y} - d + {2\sqrt{2}d}} )} + {( {w_{x} - d} )( {w_{y} - d} )}} \rbrack}};$

The four-nested-into-one ring net panel is formed by a minimum steelrope having a total mass of m_(wire)

$m_{wire} = \frac{\rho\pi d_{\min}^{2}l_{wire}}{4}$

Step (2): establishing an equivalent calculation model of the ring netpanel based on a fiber-spring unit.

Selecting a Cartesian coordinate system as a standard coordinate systemof the model, wherein h is a rising height of an edge of the loadingheading end. The net ring in the loaded region presents a rectangularshape after the deformation, and wherein a_(x) is a side length in an xdirection, a_(y) is a side length in a y direction, and axialdeformation of the net ring is ignored, then

$\{ {\begin{matrix}{{a_{1} + a_{2}} = {\pi\;{d/2}}} \\{{a_{1}/a_{2}} = {w_{2}/w_{1}}}\end{matrix};} $

the calculation model presents a biaxial symmetry. The net ring at theloaded region is straightened and intersects with an edge of the headingend having a spherical crown shape, a side length of the ring net panelin a positive half axis direction of an axis x is w_(x), intersectionpoints at intervals of a_(x) are marked as P₁, P₂ . . . P_(i) . . .P_(m), and intersection points at intervals of w_(x)(2m+1) of thecorresponding boundary are marked as Q₁, Q₂ . . . Q_(i) . . . Q_(m), andat any moment. A coordinate of a point P_(i) of an edge of the loadedregion is:

$\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} = {a_{x}( {i - {1/2}} )}} \\{{y_{P}\lbrack i\rbrack} = \sqrt{R_{P}^{2} - {a_{x}^{2}( {i - {1/2}} )}^{2}}} \\{{z_{P}\lbrack i\rbrack} = z}\end{matrix}\mspace{14mu}{and}\mspace{14mu}\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} \geq 0} \\{{y_{P}\lbrack i\rbrack} \geq 0} \\{{z_{P}\lbrack i\rbrack} \geq 0}\end{matrix};} } $

a coordinate of a point Q_(i) at the boundary may be represented as:

$\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} = {{w_{x}( {i - {1/2}} )}/( {{2m_{x}} + 1} )}} \\{{y_{Q}\lbrack i\rbrack} = {w_{y}/2}} \\{{z_{Q}\lbrack i\rbrack} = 0}\end{matrix}\mspace{14mu}{and}\mspace{14mu}\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} \geq 0} \\{{y_{Q}\lbrack i\rbrack} \geq 0} \\{{z_{Q}\lbrack i\rbrack} \geq 0}\end{matrix};} } $

wherein i=1, 2, . . . m, a calculation formula of an upper limit m takenby i is

$m = {{round}( \frac{R_{p}}{a_{1}} )}$

A position vector direction of a fiber-spring unit connecting the twopoints P_(i) and Q_(i) may be represented as an equationPQ=(x _(Q)[i]−x _(p)[i],y _(Q)[i]−y _(p)[i],−z)

in the loading process, a length value of each fiber-spring unit:L[i]=|PQ|,L ₀[i]=|PQ| _(z=0)

wherein L₀[i] is an initial length of the unit;

at any moment, a fiber length 4 and a spring length i, in the unitrespectively are:

(a)  0 < γ_(N) ≤ γ_(N 1) $\{ {\begin{matrix}{{l_{s}\lbrack i\rbrack} = \frac{{E_{f\; 1}{A( {{L\lbrack i\rbrack} - {l_{f\; 0}\lbrack i\rbrack}} )}} + {k_{s}l_{s\; 0}{l_{f\; 0}\lbrack i\rbrack}}}{{k_{s}{l_{f\; 0}\lbrack i\rbrack}} + {E_{f\; 1}A}}} \\{{l_{f}\lbrack i\rbrack} = \frac{{k_{s}{l_{f\; 0}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - l_{s\; 0}} )} + {E_{f\; 1}{{Al}_{f\; 0}\lbrack i\rbrack}}}{{k_{s}{l_{f\; 0}\lbrack i\rbrack}} + {E_{f\; 1}A}}}\end{matrix};{{(b)\mspace{14mu}\gamma_{N\; 1}} < \gamma_{N} \leq {\gamma_{N\; 2}\{ {\begin{matrix}{{l_{s}\lbrack i\rbrack} = \frac{{E_{f\; 2}{A/{l_{f\; 0}\lbrack i\rbrack}}( {{L\lbrack i\rbrack} - {l_{f\; 1}\lbrack i\rbrack}} )} + {k_{s}{l_{s\; 1}\lbrack i\rbrack}}}{k_{s} + {E_{f\; 2}{A/{l_{f\; 0}\lbrack i\rbrack}}}}} \\{{l_{f}\lbrack i\rbrack} = \frac{{k_{s}( {{L\lbrack i\rbrack} - {l_{s\; 1}\lbrack i\rbrack}} )} + {{l_{f\; 1}\lbrack i\rbrack}E_{f\; 2}{A/{l_{f\; 0}\lbrack i\rbrack}}}}{k_{s} + {E_{f\; 2}{A/{l_{f\; 0}\lbrack i\rbrack}}}}}\end{matrix};} }}} $

wherein l_(f1) and l_(s1) respectively are the fiber and spring lengthswhen γ_(N)=γ_(N1);

at any moment, an internal force value of the i^(th) fiber-spring unit

${F\lbrack i\rbrack} = \{ {\begin{matrix}{{{K_{1}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )},} & {0 < \gamma_{N} \leq \gamma_{N\; 1}} \\{{{{K_{1}\lbrack i\rbrack}( {{L_{1}\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )} + {{K_{2}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - {L_{1}\lbrack i\rbrack}} )}},} & {\gamma_{N\; 1} < \gamma_{N} \leq \gamma_{N\; 2}}\end{matrix};} $

at any moment, an energy value of the i^(th) fiber-spring unitdissipated in the loading process

${E\lbrack i\rbrack} = \{ {\begin{matrix}{{{K_{1}\lbrack i\rbrack}{( {{L\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )^{2}/2}},} & {0 < \gamma_{N} \leq \gamma_{N\; 1}} \\{\begin{matrix}{{K_{1}{L\lbrack i\rbrack}( {{L_{1}\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )} + {{K_{1}( {{L_{0}^{2}\lbrack i\rbrack} - {L_{1}^{2}\lbrack i\rbrack}} )}/}} \\{2 + {{K_{2}( {{L\lbrack i\rbrack} - {L_{1}\lbrack i\rbrack}} )}^{2}/2}}\end{matrix},} & {\gamma_{N\; 1} < \gamma_{N} \leq \gamma_{N\; 2}}\end{matrix};} $

A length of the ring net panel in a positive half axis of an axis y ismarked as w_(y), intersection points at intervals of w_(y)/(2n+1) aremarked as C₁, C₂ . . . C_(j) . . . C_(n), intersection points of thecorresponding boundary are marked as D₁, D₂ . . . D_(j) . . . D_(n).Similarly, coordinates of points C_(j) and D_(j) of the edge of theloaded region, a total length L[j] of the unit, an internal force valueF[j] of each unit, and energy dissipating E[j] at any moment may all beobtained from symmetry.

Step (3): calculating a puncturing displacement. A puncturing load andenergy dissipating of the ring net panel

In the displacement loading process of the ring net panel, when aninvalidation occurs in any fiber-spring unit of the calculation model,the net is deemed to be damaged, that is, a condition that the damageoccurs in the ring net panel is:

$\begin{matrix}{{\max\{ {{❘{F\lbrack i\rbrack}❘},{❘{F\lbrack j\rbrack}❘}} \}} = {\frac{\gamma_{Nmax}\sigma_{y}n_{w}\pi d_{\min}^{2}}{4}.}} & \end{matrix}$

Further, after step (1), the calculation method further includes:

Step (A): determining a loading rate, a loaded region and a boundarycondition of the ring net panel.

according to the geometrical parameters of the ring net panel in step(1), further determining whether the loading rate applied to the ringnet panel satisfies a quasi-static loading requirement;

judging whether a size of the loaded region satisfies a protectioncondition; and

judging that the boundary of the ring net panel is a hinged boundary oran elastic boundary.

Further, the loading rate in the step (A) refers to a moving speed of aloading heading end having a spherical crown shape in a directionvertical to a net surface of the ring net panel, and the loading rateneeds to satisfy a quasi-static condition, that is, a vertical loadingspeed is smaller than 10 mm/s;

The loaded region refers to a region where direct contact occurs betweenthe heading end having a spherical crown shape and the ring net panel,and a size of the loaded region needs to satisfy the protectioncondition, that is, a diameter D of a maximum loaded region needs to besmaller than ⅓ of a size of the ring net panel in the shortest directionMinimum{w_(x), w_(y)};

The boundary of the ring net panel may be divided into the hingedboundary or the elastic boundary. If it is the elastic boundary, anequivalent stiffness of the boundary is k_(s)=const, and if it is thehinged boundary, an equivalent stiffness of the boundary is k_(s)=∞.

Further, after step (A), the calculation method further includes:

step (B): obtaining basic mechanical parameters of materials throughtests, and establishing a critical damage criterion of the ring netpanel.

Selecting the steel rope and a steel rope net ring consistent with thegeometrical parameters in step (1) to respectively conduct a tensiletest of the steel rope and a breaking test of a three-ring ring chain.Obtaining a stress-strain curve of a material of the ring net panelthrough the test of the steel rope, to extract material parameters suchas an elastic modulus E, a yield strength σ_(y), an ultimate strengthσ_(b), a maximum plastic strain ε^(p), etc. Obtaining atension-displacement curve of a ring chain through the test of the ringchain, to extract an initial length l_(N0) of the ring chain, a lengthl_(N1) at a bent boundary moment, a tension F_(N1), an axial stressσ_(N1), a development degree of the axial stress γ_(N1), a length l_(N2)at a breaking moment, a tension F_(N2), an axial stress σ_(N2), and adevelopment degree of the axial stress γ_(N2). Obtaining the damagecriterion when puncturing occurs in the ring net panel, that is, thedevelopment degree of the maximum axial stress of the net ring in aforce transmission path of the edge of the loaded region of the ring netpanel is as follows:

$\gamma_{N\max} = {\gamma_{N2} = {\frac{\sigma_{N2}}{\sigma_{y}} = {\frac{F_{N2}}{( {2\sigma_{y}A} )}.}}}$

Further, step (3) further includes:

when a rising height of the heading end is z, as i increases (i=1, 2, 3,. . . ), the initial length L₀[i] of the fiber-spring unit increases,while the axial force F[i] of the fiber-spring unit reduces, that is,L ₀[i]<L ₀[i+1]⇒F[i+1]<F[i]

a unit having a minimum length in the model isL ₀|_(i=1)=min{L ₀[i],L ₀[j]}

that is, as for loading the displacement outside a specific surface, theinternal force of the unit (i=1) develops fastest, and the unit (i=1) isfirst damagedF| _(i=1)=γ_(N2)σ_(y) A

Thus, the length of the first damaged unit is

${ L_{\max} |_{i = 1} = {L_{0} + {\sigma_{y}{A( {\frac{\gamma_{N\; 1}}{ K_{1} |_{i = 1}} + \frac{\gamma_{N\; 2} - \gamma_{N\; 1}}{ K_{2} |_{i = 1}}} )}}}};$a length L₀ of the fiber-spring unit at a moment of z=0, a lengthL_(max) of the unit at a moment of z=H and a height H of the loadedregion at this time form a right triangle, it is obtained according tothe Pythagorean theorem that the puncturing displacement isH=z=√{square root over (L _(max) ²|_(i=1) −L ₀ ²|_(i=1))}

vectors F[i] and F[j] of the internal force of the fiber-spring unit inx and y directions and energy E[i] and E[j] dissipated by the unit maybe obtained through the symmetry, projecting all force vectors toward avertical direction, and considering the symmetry, a puncturing force ofthe ring net panel is obtained:

$\begin{matrix}{F = {4\{ {{\sum\limits_{i = 1}^{m}\frac{{F\lbrack i\rbrack}h}{L\lbrack i\rbrack}} + {\sum\limits_{j = 1}^{n}\frac{{F\lbrack j\rbrack}h}{L\lbrack j\rbrack}}} \}}} & \end{matrix}$

all energy dissipated by the fiber-spring unit are accumulated to obtainthe dissipated energy of the ring net:E=4{Σ_(i=1) ^(m) E[i]+Σ_(j=1) ^(n) E[j]}.

Further, the equivalent calculation model of the ring net panel based onthe fiber-spring unit established in the step (2) is biaxialsymmetrical. A ¼ model is considered to perform calculation andanalysis. The net ring at the loaded region is straightened andintersects with an edge of the heading end having a spherical crownshape. A side length of the ring net panel in a positive half axisdirection of the axis x is w_(x), intersection points at intervals ofa_(x) are marked as P₁, P₂ . . . P_(i) . . . P_(m), and intersectionpoints at intervals of w_(x)/(2m+1) of the corresponding boundary aremarked as Q₁, Q₂ . . . Q_(i) . . . Q_(m), and at any moment. Acoordinate of the point P_(i) of the edge of the loaded region is:

$\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} = {a_{x}( {i - {1/2}} )}} \\{{y_{P}\lbrack i\rbrack} = \sqrt{R_{P}^{2} - {a_{x}^{2}( {i - {1/2}} )}^{2}}} \\{{z_{P}\lbrack i\rbrack} = z}\end{matrix}\mspace{14mu}{and}\mspace{14mu}\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} \geq 0} \\{{y_{P}\lbrack i\rbrack} \geq 0} \\{{z_{P}\lbrack i\rbrack} \geq 0}\end{matrix};} } $

a coordinate of a point Q_(i) at the boundary may be represented as:

$\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} = {{w_{x}( {i - {1/2}} )}/( {{2m_{x}} + 1} )}} \\{{y_{Q}\lbrack i\rbrack} = {w_{y}/2}} \\{{z_{Q}\lbrack i\rbrack} = 0}\end{matrix}\mspace{14mu}{and}\mspace{14mu}\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} \geq 0} \\{{y_{Q}\lbrack i\rbrack} \geq 0} \\{{z_{Q}\lbrack i\rbrack} \geq 0}\end{matrix};} } $

wherein i=1, 2, . . . m, a calculation formula of an upper limit m takenby i is

$m = {{round}( \frac{R_{p}}{a_{1}} )}$

Since the calculation model is biaxial, the internal force anddeformation of the fiber-spring unit contained in the remaining ¾ of thering net panel may both be similarly obtained in conjunction with step(3).

Further, the puncturing displacement of the ring net panel in the step(3) refers to a difference between a height from the ground at a momentwhen the loading heading end having a spherical crown shape initiallycontacts the ring net panel and a height at a moment when the puncturingdamage occurs. The puncturing displacement depends on the deformation ofthe fiber-spring unit in the shortest force transmission path of thering net panel when the breaking occurs, and the equation of thepuncturing displacement is:H=z=√{square root over (L _(max) ²|_(i=1) −L ₀ ²|_(i=1))}

Further, the out-of-plane puncturing force of the ring net panel in thestep (3) refers to the projected accumulation values of all vectors ofthe internal force of the fiber-spring unit in the loading directionwhen the heading end having the spherical crown shape loads the ring netpanel and the puncturing damage occurs, and the equation is:

$\begin{matrix}{F = {4{\{ {{\sum\limits_{i = 1}^{m}\frac{{F\lbrack i\rbrack}h}{L\lbrack i\rbrack}} + {\sum\limits_{j = 1}^{n}\frac{{F\lbrack j\rbrack}h}{L\lbrack j\rbrack}}} \}.}}} & \end{matrix}$

Further, the energy dissipated by the ring net panel in the step (3)refers to a sum of work done by all vectors of the internal force of thefiber-spring unit in respective directions during the process that theheading end having the spherical crown shape loads the ring net panel atthe initial moment, until the puncturing damage occurs in the ring netpanel, and the equation is:E=4{Σ_(i=1) ^(m) E[i]+Σ_(j=1) ^(n) E[j]}.

Further, the high-strength steel rope in the step (1) is a basicmaterial of manufacturing the ring net panel, a surface is plated withanti-corrosion coating, and a diameter d_(min) is 2 mm-3 mm; thehigh-strength steel rope is formed to a single steel rope net ringhaving an inner diameter of d after winding a mold a certain number ofturns, and the net ring is a basic unit of the ring net panel. The ringnet panel is formed by nesting a large number of single rings in afour-nested-into-one mode, and an external contour of the ring net panelpresents a rectangle.

Compared with the prior art, the advantages of the present inventionare:

(1) the present invention firstly provides an analysis and calculationmethod of the key interception part (the ring net panel) in a passiveflexible protection system under the influence of various factors,deduces the calculation formulas of the ultimate deformation, limit loadand ultimate energy dissipating when the puncturing damage occurs in thering net panel, which is a great supplement and improvement for theexisting analysis and calculation technology of the flexible protection.

(2) The basic mechanical parameter is obtained according to the uniaxialtensile test of the steel rope material of the ring net panel, thedevelopment degree of the axial stress of the ring net panel in theshortest force transmission path is obtained through the breaking testof the three-ring ring chain and the damage criterion of the ring net isdetermined, thereby guaranteeing the accuracy of parameter values of thecalculation model and the reliability of the calculation result of themodel.

(3) Based on the load path equivalence principle, the forcecharacteristic and the damage mechanism of the ring net panel under theultimate state are specified, a three-dimensional load path equivalentmechanical model is established, thereby implementing a cross sectionequivalence of the steel rope, a vector equivalence of the forcetransmission and a region equivalence of the puncturing, which complieswith the practical damage criterion. Moreover, it is feasible in anengineering application.

(4) The calculation formulas of the ultimate deformation, load andenergy dissipating of the ring net panel are all vector operations,which is suitable for program implementation, and benefits forsimultaneously analyzing and calculating ultimate performances of thering net panel under the influence of various factors. Theimplementation process has high efficiency and accuracy.

(5) The calculation efficiency of the non-linear analysis of the ringnet panel is improved, and an analysis difficulty is reduced, therebyfacilitating the calculation and analysis for the interception parts inthe flexible protection system.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to explain the technical solutions in embodiments of thepresent invention or the prior art more clearly, a brief description ofthe drawings for the embodiments or the prior art is presented below. Itshould be noted that the following drawings are some embodiments of thepresent invention, and those ordinary technical persons skilled in theart, on the premise that no creative effort is exerted, may also obtainother drawings according to these drawings.

FIG. 1 shows a puncturing ultimate state of a ring net panel accordingto a calculation method of limit load, deformation and energydissipating of the ring net panel of a flexible protection net in thepresent application.

FIG. 2 shows a typical force-displacement curve in a tension state of aring chain according to the calculation method of limit load,deformation and energy dissipating of the ring net panel of the flexibleprotection net in the present application.

FIG. 3 shows a cross-section of a single ring according to thecalculation method of limit load, deformation and energy dissipating ofthe ring net panel of the flexible protection net in the presentapplication.

FIG. 4 shows a typical force-displacement curve in a puncturing processof the ring net panel according to the calculation method of limit load,deformation and energy dissipating of the ring net panel of the flexibleprotection net in the present application.

FIG. 5 shows the number of force vectors of a loaded region according tothe calculation method of limit load, deformation and energy dissipatingof the ring net panel of the flexible protection net in the presentapplication.

FIG. 6 is a top view of a calculation model of the ring net panelaccording to the calculation method of limit load, deformation andenergy dissipating of the ring net panel of the flexible protection netin the present application.

FIG. 7 is a main view of a calculation model of the ring net panelaccording to a calculation method of limit load, deformation and energydissipating of the ring net panel of the flexible protection net in thepresent application.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In order to clearly illustrate the purpose, technical solutions andadvantages of embodiments of the present invention, the technicalsolutions in the embodiments of the present invention will be describedclearly and completely below in conjunction with the drawings in theembodiments of the present invention, and obviously, the describedembodiments are a part of embodiments of the present invention, ratherthan the entire embodiments. Based on the embodiments of the presentinvention, all the other embodiments obtained by those ordinarytechnical persons in the art on the premise that no creative effort isexerted, belong to scopes protected by the present invention.

The analysis and calculation implementation process of the presentinvention is specifically explained below in conjunction with themechanical model which adopts the calculation method of the presentinvention. The ultimate deformation, loading and energy dissipatingabilities of the ring net panel under loading of the out-of-planequasi-static state at the shackle boundary as shown in FIG. 1 arecalculated by adopting the present invention.

As shown in FIGS. 1-7 , specific processes of the calculation method ofthe limit load, deformation and energy dissipating of the ring net panelof the present invention are as follows:

Step (1): geometrical parameters of the ring net panel, a nested netring, and a wound steel rope are determined.

A side length of a square ring net panel is w₀=3.0 m, an inner diameterof the net ring in the ring net panel is d=300 mm, and each net ring isformed by winding the steel rope having a diameter of d_(min)=3.0 mm andn_(w)=7 turns. The boundary of the ring net panel adopts a shackle tohinge, and an equivalent boundary rigidity is k_(s)=∞. The loaded regionof the ring net panel is circular, a diameter of a loading apparatus isD=1.0 m, the loaded position is located at a geometrical center of thering net panel, and a loading direction is vertical to a net surfacedirection.

A cross-section area of the single net ring is A

$A = {\frac{7\pi \times {0.0}03^{2}}{4} = {{4.9}48 \times 10^{- 5}m^{2}}}$

The ring net panel (nesting mode: four-nested-into-one) is formed by aminimum steel rope having a total length of l_(wire)

$l_{wire} = {{\frac{7\pi \times 0.3}{2\sqrt{2} \times 0.3}\lbrack {( {3 - 0.3 + {2\sqrt{2} \times 0.3}} )^{2} + ( {3 - 0.3} )^{2}} \rbrack} = {145.02m}}$

The ring net panel (nesting mode: four-nested-into-one) is formed by aminimum steel rope having a total mass of m_(wire)

$m_{wire} = {\frac{7850 \times \pi \times {0.0}03^{2} \times 14{5.0}2}{4} = {8.05{kg}}}$

Step (A): a loading rate, a loaded region and a boundary condition ofthe ring net panel are determined.

According to the geometrical parameters of the ring net panel in step(1), the loading rate of v=7 min/s<10 mm/s applied to the ring net panelis further determined, which satisfies a quasi-static loading condition.The diameter of the maximum loaded region is D=1.0 m≤w₀/3, whichsatisfies a safety protection requirement. The boundary equivalentspring rigidity of the ring net panel is k_(s)=∞, and an initial lengthof the spring is l_(s0)=0.05 m.

Step (B): basic mechanical parameters of materials are obtained throughtests, and a critical damage criterion of the ring net panel isestablished.

The steel rope (a diameter is d_(min)=3.0 mm) and a steel rope net ring(the winding number of turns of the steel rope is n_(w)=7, an innerdiameter of the net ring is d=0.3 m) consistent with the geometricalparameters in step (1) are selected to respectively conduct a tensiletest of the steel rope and a breaking test of a three-ring ring chain. Astress-strain curve of the ring net panel material is obtained throughthe test of the steel rope, to obtain an elastic modulus E=150 GPa ofthe steel rope, a yield strength being σ_(y)=1770 MPa, an ultimatestrength being σ_(b)=1850 MPa, a maximum plastic strain beingε^(p)=0.05. A tension-displacement curve of a ring chain is obtainedthrough the test of the ring chain, to extract an initial lengthl_(N0)=0.9 m of the ring chain, a length l_(N1)=1.327 m at a bentboundary moment, a tension F_(N1)=11.011 kN, a development degree of theaxial stress γ_(N1)=0.063, a length l_(N2)=1.403 m at a breaking moment,a tension F_(N2)=73.410 kN, and a development degree of the axial stressγ_(N2)=0.419. As shown in FIGS. 1, 2 and 4 , the change of an axialtensile rigidity in the ring chain stretching process features twostages, the steel rope ring chain is equivalent to fiber deformation,and rigidities at the two stages respectively are

$\{ {\begin{matrix}{{E_{f1} = {\frac{11.011 \times 0.9}{2 \times 4.948 \times 10^{- 5} \times ( {1.327 - 0.9} )} = {234.52{MPa}}}},} & {0 < \gamma_{N} \leq \gamma_{N1}} \\{{E_{f2} = {\frac{( {73.41 - 11.011} ) \times 0.9}{2 \times 4.948 \times 10^{- 5} \times ( {1.403 - 1.327} )} = {7523.068{MPa}}}},} & {\gamma_{N1} < \gamma_{N} \leq \gamma_{N2}}\end{matrix}} $

The damage criterion when the puncturing occurs in the ring net panel isobtained simultaneously, that is, the development degree of the maximumaxial stress of the net ring in a force transmission path of the loadedregion edge of the ring net panel is as follows:

$\gamma_{N\max} = {\frac{\sigma_{N2}}{\sigma_{y}} = {{0.4}0}}$

Step (2): an equivalent calculation model of the ring net panel based ona fiber-spring unit is established.

A Cartesian coordinate system (xyz) is selected as a standard coordinatesystem of the model. h is a rising height of a top of the loaded end.The net ring in the loaded region presents a rectangle after thedeformation (a_(x) is a side length in an x direction, a_(y) is a sidelength in a y direction), and axial deformation of the net ring isignored, then

$\{ {{\begin{matrix}{{a_{x} + a_{y}} = {0.3{\pi/2}}} \\{{a_{x}/a_{y}} = 1}\end{matrix}a_{x}} = {a_{y} = {0.2356m}}} $

The calculation model presents a biaxial symmetry, the net ring of theloaded region is straightened and intersects with an edge of the headingend having a spherical crown shape, a side length of the ring net panelin a positive half axis direction of an axis x is w_(x), intersectionpoints at intervals of _(a)x are marked as P₁, P₂ . . . P_(i) . . .P_(m), and intersection points at intervals of w_(x)/(2m+1) of thecorresponding boundary are marked as Q₁, Q₂ . . . Q_(i) . . . Q_(m),wherein i=1, 2, . . . m, a calculation formula of an upper limit m takenby i is

$m = {{{round}( \frac{0.5}{{0.2}356} )} = 2}$

a coordinate of a point P₁ of the edge of the loaded region is:

$\{ {\begin{matrix}{{x_{P}\lbrack 1\rbrack} = {{0.2356 \times ( {1 - {1/2}} )} = {0.1178m}}} \\{{y_{P}\lbrack 1\rbrack} = {\sqrt{0.5^{2} - {0.2356^{2} \times ( {1 - {1/2}} )^{2}}} = {0.4859m}}} \\{{z_{P}\lbrack 1\rbrack} = z}\end{matrix}} $

a coordinate of a point Q₁ of the boundary position may be representedas:

$\{ {\begin{matrix}{{x_{Q}\lbrack 1\rbrack} = {{2.95 \times {( {1 - {1/2}} )/( {{2 \times 2} + 1} )}} = {0.295m}}} \\{{y_{Q}\lbrack 1\rbrack} = {{2.95/2} = {1.475m}}} \\{{z_{Q}\lbrack 1\rbrack} = 0}\end{matrix}} $

a coordinate of a point P₂ of the edge of the loaded region is:

$\{ {\begin{matrix}{{x_{P}\lbrack 2\rbrack} = {{0.2356 \times ( {2 - {1/2}} )} = {0.3534m}}} \\{{y_{P}\lbrack 2\rbrack} = {\sqrt{0.5^{2} - {0.2356^{2} \times ( {2 - {1/2}} )^{2}}} = {0.3537m}}} \\{{z_{P}\lbrack 2\rbrack} = z}\end{matrix}} $

a coordinate of a point at Q₂ of the boundary may be represented a:

$\{ {\begin{matrix}{{x_{Q}\lbrack 2\rbrack} = {{2.95 \times {( {2 - {1/2}} )/( {{2 \times 2} + 1} )}} = {0.885m}}} \\{{y_{Q}\lbrack 2\rbrack} = {{2.95/2} = {1.475m}}} \\{{z_{Q}\lbrack 2\rbrack} = 0}\end{matrix}} $

a position vector matrix of a fiber-spring unit connecting P_(i) andQ_(i) may be represented as

${PQ} = \begin{bmatrix}0.1772 & 0.9891 & {- z} \\0.3516 & 1.1213 & {- z}\end{bmatrix}^{T}$

at any moment, a length value of each fiber-spring unit:L[1]=√{square root over (0.1772²+0.9891² +z ²)}L[2]=√{square root over (0.3516²+1.1213² +z ²)}

at an initial moment z=0, a length value L₀[i] of each fiber-spring unitis:L ₀[1]=√{square root over (0.1772²+0.9891² +z ²)}|_(z=0)=1.0048 mL ₀[2]=√{square root over (0.3516²+1.1213² +z ²)}|_(z=0)=1.2409 m

at any moment, a fiber length l_(f) and a spring length l_(s) in thei^(th) unit (i=1, 2) respectively are

(a)  0 < γ_(N) ≤ γ_(N 1) $\{ {{\begin{matrix}{{l_{s}\lbrack 1\rbrack} = \frac{{E_{f\; 1}{A( {{L\lbrack 1\rbrack} - {l_{f\; 0}\lbrack 1\rbrack}} )}} + {k_{s}l_{s\; 0}{l_{f\; 0}\lbrack 1\rbrack}}}{{k_{s}{l_{f\; 0}\lbrack i\rbrack}} + {E_{f\; 1}A}}} \\{{l_{f}\lbrack 1\rbrack} = \frac{{k_{s}{l_{f\; 0}\lbrack 1\rbrack}( {{L\lbrack 1\rbrack} - l_{s\; 0}} )} + {E_{f\; 1}{{Al}_{f\; 0}\lbrack 1\rbrack}}}{{k_{s}{l_{f\; 0}\lbrack 1\rbrack}} + {E_{f\; 1}A}}}\end{matrix}(b)\mspace{14mu}\gamma_{N\; 1}} < \gamma_{N} \leq {\gamma_{N\; 2}\{ \begin{matrix}{{l_{s}\lbrack 1\rbrack} = \frac{{E_{f\; 2}{A/{l_{f\; 0}\lbrack 1\rbrack}}( {{L\lbrack 1\rbrack} - {l_{f\; 1}\lbrack 1\rbrack}} )} + {k_{s}{l_{s\; 1}\lbrack 1\rbrack}}}{k_{s} + {E_{f\; 2}{A/{l_{f\; 0}\lbrack 1\rbrack}}}}} \\{{l_{f}\lbrack 1\rbrack} = \frac{{k_{s}( {{L\lbrack 1\rbrack} - {l_{s\; 1}\lbrack 1\rbrack}} )} + {{l_{f\; 1}\lbrack 1\rbrack}E_{f\; 2}{A/{l_{f\; 0}\lbrack 1\rbrack}}}}{k_{s} + {E_{f\; 2}{A/{l_{f\; 0}\lbrack 1\rbrack}}}}}\end{matrix} }} $

wherein l_(f1) and l_(s1) respectively are the fiber and spring lengthswhen γ_(N)=γ_(N1).

The boundary spring is connected to the equivalent fiber in series,combination rigidities of the first (i=1) fiber-spring unit at twostages respectively are

$\{ {\begin{matrix}{{{K_{1}\lbrack 1\rbrack} = {{1/\lbrack {{{l_{f\; 0}\lbrack 1\rbrack}/( {E_{f\; 1}A} )} + {1/k_{s}}} \rbrack} = {12.141\mspace{14mu}{kN}\text{/}m}}},} & {0 < \gamma_{N} \leq \gamma_{{N\; 1}\;}} \\{{{K_{2}\lbrack 1\rbrack} = {{1/\lbrack {{{l_{f\; 0}\lbrack 1\rbrack}/( {E_{f\; 2}A} )} + {1/k_{s}}} \rbrack} = {389.854\mspace{14mu}{kN}\text{/}m}}},} & {\gamma_{N\; 1} < \gamma_{N} \leq \gamma_{N\; 2}}\end{matrix}\quad} $

combination rigidities of the second (i=2) fiber-spring unit at twostages respectively are

$\{ {\begin{matrix}{{{K_{1}\lbrack 2\rbrack} = {{1/\lbrack {{{l_{f\; 0}\lbrack 2\rbrack}/( {E_{f\; 1}A} )} + {1/k_{s}}} \rbrack} = {9.733\mspace{14mu}{kN}\text{/}m}}},} & {0 < \gamma_{N} \leq \gamma_{{N\; 1}\;}} \\{{{K_{2}\lbrack 2\rbrack} = {{1/\lbrack {{{l_{f\; 0}\lbrack 2\rbrack}/( {E_{f\; 2}A} )} + {1/k_{s}}} \rbrack} = {312.561\mspace{14mu}{kN}\text{/}m}}},} & {\gamma_{N\; 1} < \gamma_{N} \leq \gamma_{N\; 2}}\end{matrix}\quad} $

at any moment, an internal force value of the i^(th) fiber-spring unit(i=1, 2) is as follows:

${F\lbrack i\rbrack} = \{ \begin{matrix}{{{K_{1}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )},} & {0 < \gamma_{N} \leq \gamma_{N\; 1}} \\{{{{K_{1}\lbrack i\rbrack}( {{L_{1}\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )} + {{K_{2}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - {L_{1}\lbrack i\rbrack}} )}},} & {\gamma_{N\; 1} < \gamma_{N} \leq \gamma_{N\; 2}}\end{matrix} $at any moment, an energy value of the i fiber-spring unit i=1, 2dissipated in the loading process is as follows:

${E\lbrack i\rbrack} = \{ \begin{matrix}{{{K_{1}\lbrack i\rbrack}{( {{L\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )^{2}/2}},} & {0 < \gamma_{N} \leq \gamma_{N\; 1}} \\{\begin{matrix}{{K_{1}{L\lbrack i\rbrack}( {{L_{1}\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )} + {{K_{1}( {{L_{0}^{2}\lbrack i\rbrack} - {L_{1}^{2}\lbrack i\rbrack}} )}/}} \\{2 + {{K_{2}( {{L\lbrack i\rbrack} - {L_{1}\lbrack i\rbrack}} )}^{2}/2}}\end{matrix},} & {\gamma_{N\; 1} < \gamma_{N} \leq \gamma_{N\; 2}}\end{matrix} $

a length of the ring net panel in a positive half axis of an axis y ismarked as w₀, intersection points at intervals of w₀/(2m+1) are markedas C₁, C₂ . . . C_(j) . . . C_(n), intersection points of thecorresponding boundary are marked as D₁, D₂ . . . D_(j) . . . D_(n).Similarly, coordinates of points C, and D_(j) of the edge of the loadedregion, a total length L[j] of the unit, an internal force value F[j] ofeach unit, and energy dissipating E[j] at any moment may all be obtainedfrom symmetry.

step (3): calculating a puncturing displacement, a puncturing load andenergy dissipating of the ring net panel.

In the displacement loading process of the ring net panel, when aninvalidation occurs in any fiber-spring unit of the calculation model,the ring net panel is damaged, that is, a condition that damage occursin the ring net panel is:

$\begin{matrix}{{\max\{ {{❘{F\lbrack i\rbrack}❘},{❘{F\lbrack j\rbrack}❘}} \}} = {\frac{{0.4}19 \times 1770 \times 7 \times \pi \times 3^{2}}{4} = {3{6.6}96{kN}}}} & \end{matrix}$

a unit having a minimum length in the model isL ₀|_(i=1)=min{L ₀[i],L ₀[j]}=1.005 m

that is, as for loading the displacement outside a specific surface, theinternal force of the unit (i=1) develops fastest, and the unit (i=1) isfirst damagedF| _(i=1)=γ_(N2)σ_(y) A=36.396 kN

Thus, the length of the first damaged unit is

${L_{\max}}_{i = 1} = {{1.005 + {1770 \times 49.48 \times ( {\frac{0.063}{12140} + \frac{0.149 - 0.063}{389854}} )}} = {1.539\mspace{14mu} m}}$

A length L₀ of the fiber-spring unit at a moment of z=0, a lengthL_(max) of the unit at a moment of z=H and a height H of the loadedregion at this time form a right triangle. According to the Pythagoreantheorem, the puncturing displacement (a height of the loaded region) isH=z=√{square root over (1.539²−1.005²)}=1.165 m

When the puncturing occurs in the ring net panel, z=1.165 is substitutedinto the equation of F[i]:F[1]=K ₁[1](L ₁[1]−L ₀[1])+K ₂[1](L[1]−L ₁[1])=36.705 kNF[2]=K ₁[2](L ₁[2]−L ₀[2])+K ₂[2](L[2]−L ₁[2])=26.283 kN

z=1.165 is substituted into the equation of E[i]:

$\begin{matrix}{{{E\lbrack 1\rbrack} = {{{K_{1}{L( {{L_{1}\lbrack 1\rbrack} - {L_{0}\lbrack 1\rbrack}} )}} + \frac{K_{1}( {{L_{0}^{2}\lbrack 1\rbrack} - {L_{1}^{2}\lbrack 1\rbrack}} )}{2} + \frac{{K_{2}( {{L\lbrack 1\rbrack} - {L_{1}\lbrack 1\rbrack}} )}^{2}}{2}} = {2.937{kJ}}}}{{E\lbrack 2\rbrack} = {{{K_{1}{L\lbrack 2\rbrack}( {{L_{1}\lbrack 2\rbrack} - {L_{0}\lbrack 2\rbrack}} )} + \frac{K_{1}( {{L_{0}^{2}\lbrack 2\rbrack} - {L_{1}^{2}\lbrack 2\rbrack}} )}{2} + \frac{{K_{2}( {{L\lbrack 2\rbrack} - {L_{1}\lbrack 2\rbrack}} )}^{2}}{2}} = {{1.8}19{}{kJ}}}}} & \lbrack 2\rbrack\end{matrix}$

a vector F[i] and F[j] of the internal force of the fiber-spring unit inx and y directions and an energy E[i] and E[j] dissipated by the unitmay be obtained through the symmetry, wherein F[i]=F[j], and E[i]=E[j].All force vectors are projected toward a vertical direction, andconsidering the symmetry, a puncturing force of the ring net panel is asfollows:

$\begin{matrix}{F = {{4\{ {{\sum\limits_{i = 1}^{m}\frac{{F\lbrack i\rbrack}h}{L\lbrack i\rbrack}} + {\sum\limits_{j = 1}^{n}\frac{ {F\lceil j } \rbrack h}{L\lbrack j\rbrack}}} \}} = {36{6.2}47{kN}}}} & \end{matrix}$

all energy dissipated by the fiber-spring unit is accumulated to obtainthe dissipated energy of the ring net as follows:

$E = {{4\{ {{\sum\limits_{i = 1}^{m}{E\lbrack i\rbrack}} + {\sum\limits_{j = 1}^{n}{E\lbrack j\rbrack}}} \}} = {38.05{kJ}}}$

When the ring net panels in the passive flexible protection net areconnected by aluminum-alloy swaged ferrules, it should comply with theprovision of “Aluminum-alloy swaged ferrules for steel wire rope” GB/T6946-2008. When the ring net panels are connected by the shackle, itshould comply with the provision of “Forged shackles for general liftingpurposes-Dee shackles and bow shackles” GB/T 25854-2010.

The above embodiments are only used to explain the technical solutionsof the present invention, rather than limiting them. Although thepresent invention is specifically explained referring to the previousembodiments, those ordinary technical persons in the art shouldunderstand that they still may amend the technical solutions recorded inthe previous respective embodiments, or perform equivalent replacementsfor partial technical features therein. These amendments or replacementsdo not make the nature of the corresponding technical solutions departfrom the spirits and scopes of the technical solutions of the respectiveembodiments of the present invention.

What is claimed is:
 1. A method of a quantitative analysis and a designof a reliable flexible protection net by determining a limit load, adeformation, and an energy dissipating of the flexible protection net tomeet safety protection requirements, wherein the flexible protection netcomprises a ring net panel and a support part, wherein the support parthas a protection structure, wherein the ring net panel is connected tothe support part through a shackle and a steel rope, and wherein thering net panel is a nesting of a plurality of single rings, the methodcomprising: step (1): determining geometrical parameters of the ring netpanel, the nested net ring, and the steel rope, wherein an innerdiameter of each single ring of the plurality of single rings is d, eachsingle ring is manufactured by winding the steel rope having a diameterof d_(min) to form different numbers of turns n_(w), and across-sectional area of the single ring it A${A = \frac{n_{w}\pi d_{\min}^{2}}{4}};$ the ring net panel has a lengthw_(x) and a width w_(y), a four-nested-into-one ring net panel is formedby using a minimum steel rope having a total length of l_(wire)${l_{wire} = {\frac{n_{w}\pi d}{2\sqrt{2}d}\lbrack {{( {w_{x} - d + {2\sqrt{2}d}} )( {w_{y} - d + {2\sqrt{2}d}} )} + {( {w_{x} - d} )( {w_{y} - d} )}} \rbrack}};$the four-nested-into-one ring net panel is formed by the minimum steelrope having a total mass of m_(wire); step (2): establishing anequivalent calculation model of the ring net panel based on a fiberspring, wherein a Cartesian coordinate system is selected as a standardcoordinate system of the equivalent calculation model, h is a risingheight of a loading heading end, a net ring in a loaded region isrectangular after deformation, a_(x) is a side length of the net ring inan x direction, a_(y) is a side length of the net ring in a y direction,and axial deformation of the net ring is ignored, then$\{ {\begin{matrix}{{a_{1} + a_{2}} = {\pi{d/2}}} \\{{a_{1}/a_{2}} = {w_{2}/w_{1}}}\end{matrix}{;}} $ the equivalent calculation model presents abiaxial symmetry, the net ring of the loaded region is straightened andintersects with an edge of the loading heading end having a sphericalcrown shape, a side length of the ring net panel in a positive half axisdirection of an axis x is w_(x), first intersection points at intervalsof a_(x) are marked as P₁, P₂ . . . P_(i) . . . P_(m), and secondintersection points at intervals of w_(x)/(2m+1) of a boundarycorresponding to the side length of the ring net panel are marked as Q₁,Q₂ . . . Q_(i) . . . Q_(m), and at any moment, a coordinate of a pointP_(i) of an edge of the loaded region is: $\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} = {a_{x}( {i - {1/2}} )}} \\{{y_{P}\lbrack i\rbrack} = \sqrt{R_{p}^{2} - {a_{x}^{2}( {i - {1/2}} )}^{2}}} \\{{z_{P}\lbrack i\rbrack} = z}\end{matrix}{and}\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} \geq 0} \\{{y_{P}\lbrack i\rbrack} \geq 0} \\{{z_{P}\lbrack i\rbrack} \geq 0}\end{matrix};} } $ a coordinate of a point Q_(i) at theboundary is: $\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} = {{w_{x}( {i - {1/2}} )}/( {{2m_{x}} + 1} )}} \\{{y_{Q}\lbrack i\rbrack} = {w_{y}/2}} \\{{z_{Q}\lbrack i\rbrack} = 0}\end{matrix}{and}\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} \geq 0} \\{{y_{Q}\lbrack i\rbrack} \geq 0} \\{{z_{Q}\lbrack i\rbrack} \geq 0}\end{matrix};} } $ wherein i=1, 2, . . . m, m is an upperlimit of i; a position vector direction of the fiber spring connectingthe point P_(i) and the point Q_(i) is represented as the followingequation:PQ=(x _(Q)[i]−x _(p)[i],y _(Q)[i]−y _(p)[i],−z) in a loading process, alength value of a i^(th) fiber spring is:L[i]=|PQ|,L ₀[i]=|PQ| _(z=0) ; wherein L₀[i] is an initial length of thei^(th) fiber spring; at any moment, a fiber length l_(f) and a springlength l_(s) in the i^(th) fiber spring respectively are:${(a)0} < \gamma_{N} \leq {\gamma_{N1}\{ {\begin{matrix}{{l_{s}\lbrack i\rbrack} = \frac{{E_{f1}{A( {{L\lbrack i\rbrack} - {l_{f0}\lbrack i\rbrack}} )}} + {k_{s}l_{s0}{l_{f0}\lbrack i\rbrack}}}{{k_{s}{l_{f0}\lbrack i\rbrack}} + {E_{f1}A}}} \\{{l_{f}\lbrack i\rbrack} = \frac{{k_{s}{l_{f0}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - l_{f0}} )} + {E_{f1}{{Al}_{f0}\lbrack i\rbrack}}}{{k_{s}{l_{f0}\lbrack i\rbrack}} + {E_{f1}A}}}\end{matrix};{{(b)\gamma_{N1}} < \gamma_{N} \leq {\gamma_{N2}\{ {\begin{matrix}{{l_{s}\lbrack i\rbrack} = \frac{{E_{f2}{A/{l_{f0}\lbrack i\rbrack}}( {{L\lbrack i\rbrack} - {l_{f1}\lbrack i\rbrack}} )} + {k_{s}{l_{s1}\lbrack i\rbrack}}}{k_{s} + {E_{f2}{A/{l_{f0}\lbrack i\rbrack}}}}} \\{{l_{f}\lbrack i\rbrack} = \frac{{k_{s}( {{L\lbrack i\rbrack} - {l_{s1}\lbrack i\rbrack}} )} + {{l_{f1}\lbrack i\rbrack}E_{f2}{A/{l_{f0}\lbrack i\rbrack}}}}{k_{s} + {E_{f2}{A/{l_{f0}\lbrack i\rbrack}}}}}\end{matrix};} }}} }$ wherein l_(f1) is the fiber length;l_(s1) is the spring length when γ_(N)=γ_(N1); γ_(N) is a developmentdegree of an axial stress; γ_(N1) is a development degree of a firstaxial stress σ_(N1); and γ_(N2) is a development degree of a secondaxial stress σ_(N2); at any moment, an internal force value of thei^(th) fiber spring ${F\lbrack i\rbrack} = \{ {\begin{matrix}{{{K_{1}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )},} & {0 < \gamma_{N} \leq \gamma_{N1}} \\{{{{K_{1}\lbrack i\rbrack}( {{L_{1}\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )} + {{K_{2}\lbrack i\rbrack}( {{L\lbrack i\rbrack} - {L_{1}\lbrack i\rbrack}} )}},} & {\gamma_{N1} < \gamma_{N} \leq \gamma_{N2}}\end{matrix};} $ at any moment, an energy value of the i^(th)fiber spring dissipated in the loading process${E\lbrack i\rbrack} = \{ {\begin{matrix}{{{K_{1}\lbrack i\rbrack}{( {{L\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )^{2}/2}},} & {0 < \gamma_{N} \leq \gamma_{N1}} \\\begin{matrix}{{K_{1}{L\lbrack i\rbrack}( {{L_{1}\lbrack i\rbrack} - {L_{0}\lbrack i\rbrack}} )} + {{K_{1}( {{L_{0}^{2}\lbrack i\rbrack} - {L_{1}^{2}\lbrack i\rbrack}} )}/2} +} \\{{{K_{2}( {{L\lbrack i\rbrack} - {L_{1}\lbrack i\rbrack}} )}^{2}/2},}\end{matrix} & {\gamma_{N1} < \gamma_{N} \leq \gamma_{N2}}\end{matrix};} $ a length of the ring net panel in a positivehalf axis of an axis y is marked as w_(y), third intersection points atintervals of w_(y)/(2n+1) are marked as C₁, C₂ . . . C_(j) . . . C_(n),fourth intersection points of the boundary corresponding to the lengthof the ring net panel are marked as D₁, D₂ . . . D_(j) . . . D_(n);similarly, coordinates of points C_(j) and D_(j) of the edge of theloaded region, a total length L[j] of the j^(h) fiber spring, theinternal force value F[j] of the j^(h) fiber spring, and an energydissipating E[j] at any moment are obtained from symmetry; step (3):calculating a puncturing displacement, a puncturing load and the energydissipating of the ring net, wherein in a displacement process and theloading process of the ring net panel, when an invalidation occurs inany fiber spring of the equivalent calculation model, the ring net panelis damaged, a damage occurrence condition the ring net panel is:$\begin{matrix}{{{\max\{ {{❘{F\lbrack i\rbrack}❘},{❘{F\lbrack j\rbrack}❘}} \}} = \frac{\gamma_{N\max}\sigma_{y}n_{w}\pi d_{\min}^{2}}{4}},{and}} & \end{matrix}$ step (4): designing the reliable flexible protection netto improve the performance of the net in interception effect using theparameters calculated in previous steps that satisfy safety protectionrequirements.
 2. The method according to claim 1, wherein, after step(1), the method further comprises: step (A): determining a loading rate,the loaded region and a boundary condition of the ring net panel,wherein according to the geometrical parameters of the ring net panel instep (1), whether the loading rate applied to the ring net panelsatisfies a quasi-static loading requirement is further determined;whether a size of the loaded region satisfies a protection condition isjudged; and whether a boundary of the ring net panel is a hingedboundary or an elastic boundary is judged.
 3. The method according toclaim 2, wherein the loading rate in the step (A) is a moving speed ofthe loading heading end having the spherical crown shape in a directionvertical to a net surface of the ring net panel, and the loading ratesatisfies the quasi-static loading requirement, wherein, thequasi-static loading requirement is that a vertical loading rate of theloading heading end is smaller than 10 mm/s; the loading heading endhaving the spherical crown shape directly comes in contact with the ringnet panel at the loaded region, and the size of the loaded regionsatisfies the protection condition, wherein, the protection condition isthat a diameter D of a maximum loaded region is smaller than ⅓ of a sizeof the ring net panel in a shortest direction Minimum{w_(x), w_(y)}; theboundary of the ring net panel comprises the hinged boundary or theelastic boundary, if the boundary of the ring net panel is the elasticboundary, an equivalent stiffness of the boundary is k_(s)=const, and ifthe boundary of the ring net panel is the hinged boundary, an equivalentstiffness of the boundary is k_(s)=∞.
 4. The method according to claim2, wherein, after step (A), the method further comprises: step (B):obtaining basic mechanical parameters of materials through tests, andestablishing a critical damage criterion of the ring net panel, whereinthe steel rope and a steel rope net ring consistent with the geometricalparameters in step (1) are selected to respectively conduct a tensiletest of the steel rope and a breaking test of a three-ring ring chain; astress-strain curve of the ring net panel material is obtained throughthe tensile test of the steel rope, to extract material parameters suchas an elastic modulus E, a yield strength σ_(y), an ultimate strengthσ_(b), a maximum plastic strain ε^(p), etc.; a tension-displacementcurve of a ring chain is obtained through the breaking test of thethree-ring ring chain, to extract an initial length l_(N0) of the ringchain, a length l_(N1) at a bent boundary moment, a tension F_(N1), alength l_(N2) at a breaking moment, and a tension F_(N2); the criticaldamage criterion when puncturing occurs in the ring net panel isobtained, wherein, the critical damage criterion is that the developmentdegree of a maximum axial stress of the net ring in a force transmissionpath of the edge of the loaded region of the ring net panel is:$\gamma_{N\max} = {\gamma_{N2} = {\frac{\sigma_{N2}}{\sigma_{y}} = {\frac{F_{N2}}{( {2\sigma_{y}A} )}.}}}$5. The method according to claim 1, wherein, step (3) further comprises:when a rising height of the loading heading end is z, as i increases(i=1, 2, 3, . . . ), an initial length L₀[i] of the fiber springincreases, while an axial force F[i] of the fiber spring reduces,L ₀[i]<L ₀[i+1]⇒F[i+1]<F[i]; the fiber spring having a minimum length inthe equivalent calculation model isL ₀|_(i=1)=min{L ₀[i],L ₀[j]}; when a displacement is loaded outside aspecific surface, an internal force of the fiber spring (i=1) developsfastest, and the fiber spring (i=1) is first damagedF| _(i=)1=γ_(N2)σ_(y) A; a length of the fiber spring first damaged is${L_{{\max|i} = 1} = {L_{0} + {\sigma_{y}{A( {\frac{\gamma_{N1}}{ K_{1} |_{i = 1}} + \frac{\gamma_{N2} - \gamma_{N1}}{ K_{2} |_{i = 1}}} )}}}};$a length L₀ of the fiber spring at a moment of z=0, a length L_(max) ofthe fiber spring at a moment of z=H and a height H of the loaded regionat the moment of z=H form a right triangle; according to the Pythagoreantheorem, the puncturing displacement isH=z=√{square root over (L _(max) ²|_(i=1) −L ₀ ²|_(i=1))} vectors F[i]and F[j] of the internal force of the fiber spring in x and y directionsand energy E[i] and E[j] dissipated by the fiber spring are obtainedthrough the symmetry, projecting all force vectors toward a verticaldirection, and considering the symmetry, a puncturing force of the ringnet panel is as follows: $\begin{matrix}{{F = {4\{ {{\sum\limits_{i = 1}^{m}\frac{{F\lbrack i\rbrack}h}{L\lbrack i\rbrack}} + {\sum\limits_{j = 1}^{n}\frac{{F\lbrack j\rbrack}h}{L\lbrack j\rbrack}}} \}}};} & \end{matrix}$ all energy dissipated by the fiber spring are accumulatedto obtain the dissipating energy of the ring net:E=4{Σ_(i=1) ^(m) E[i]+Σ_(j=1) ^(n) E[j]}.
 6. The method according toclaim 1, wherein the equivalent calculation model of the ring net panelbased on the fiber spring established in the step (2) is biaxiallysymmetrical, the net ring of the loaded region is straightened andintersects with an edge of the loading heading end having the sphericalcrown shape, the side length of the ring net panel in the positive halfaxis direction of the axis x is w_(x), the first intersection points atintervals of a_(x) are marked as P₁, P₂ . . . P_(i) . . . P_(m), and thesecond intersection points at intervals of w_(x)/(2m+1) of the boundarycorresponding to the side length of the ring net panel are marked as Q₁,Q₂ . . . Q_(i) . . . Q_(m), and at any moment, the coordinate of thepoint P_(i) of the edge of the loaded region is:$\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} = {a_{x}( {i - {1/2}} )}} \\{{y_{P}\lbrack i\rbrack} = \sqrt{R_{p}^{2} - {a_{x}^{2}( {i - {1/2}} )}^{2}}} \\{{z_{P}\lbrack i\rbrack} = z}\end{matrix}{and}\{ {\begin{matrix}{{x_{P}\lbrack i\rbrack} \geq 0} \\{{y_{P}\lbrack i\rbrack} \geq 0} \\{{z_{P}\lbrack i\rbrack} \geq 0}\end{matrix};} } $ the coordinate of the of point Q_(i) atthe boundary is: $\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} = {{w_{x}( {i - {1/2}} )}/( {{2m_{x}} + 1} )}} \\{{y_{Q}\lbrack i\rbrack} = {w_{y}/2}} \\{{z_{Q}\lbrack i\rbrack} = 0}\end{matrix}{and}\{ {\begin{matrix}{{x_{Q}\lbrack i\rbrack} \geq 0} \\{{y_{Q}\lbrack i\rbrack} \geq 0} \\{{z_{Q}\lbrack i\rbrack} \geq 0}\end{matrix};} } $ wherein i=1, 2, . . . m, m is the upperlimit of i.
 7. The method according to claim 5, wherein the puncturingdisplacement of the ring net panel in the step (3) is a differencebetween a height from the ground at a moment when the loading headingend having the spherical crown shape initially contacts the ring netpanel and a height at a moment when puncturing damage occurs, thepuncturing displacement depends on the deformation of the fiber springin a shortest force transmission path of the ring net panel when thebreaking occurs, and an equation of the puncturing displacement is:H=z=√{square root over (L _(max) ²|_(i=1) −L ₀ ²|_(i=1))}.
 8. The methodaccording to claim 5, wherein the puncturing force of the ring net panelin the step (3) is a projected accumulation value of all vectors of theinternal force of the fiber spring in a loading direction when theloading heading end having the spherical crown shape loads the ring netpanel and puncturing damage occurs, and an equation is: $\begin{matrix}{F = {4{\{ {{\sum\limits_{i = 1}^{m}\frac{{F\lbrack i\rbrack}h}{L\lbrack i\rbrack}} + {\sum\limits_{j = 1}^{n}\frac{{F\lbrack j\rbrack}h}{L\lbrack j\rbrack}}} \}.}}} & \end{matrix}$
 9. The method according to claim 5 wherein the energydissipated by the ring net panel in the step (3) is a sum of work doneby all vectors of the internal force of the fiber spring in respectivedirections during the loading process from the initial moment to apuncturing moment, wherein the loading heading end having the sphericalcrown shape loads the ring net panel at the initial moment, andpuncturing damage occurs in the ring net panel at the puncturing moment,and an equation is:E=4{Σ_(i=1) ^(m) E[i]+Σ_(j=1) ^(n) E[j]}.
 10. The method according toclaim 1, wherein the steel rope having high strength in the step (1) isa basic material of manufacturing the ring net panel, a surface of thesteel rope is plated with anti-corrosion coating, and a diameter d_(min)of the steel rope is 2 mm-3 mm; the steel rope having high strength isformed to a single steel rope net ring having the inner diameter of dafter winding a mold a certain number of turns, and the net ring is abasic unit of the ring net panel; the ring net panel is formed bynesting the plurality of single rings in a four-nested-into-one mode,and an external contour of the ring net panel is rectangular.
 11. Themethod according to claim 3, wherein, after step (A), the method furthercomprises: step (B): obtaining basic mechanical parameters of materialsthrough tests, and establishing a critical damage criterion of the ringnet panel, wherein the steel rope and a steel rope net ring consistentwith the geometrical parameters in step (1) are selected to respectivelyconduct a tensile test of the steel rope and a breaking test of athree-ring ring chain; a stress-strain curve of the ring net panelmaterial is obtained through the tensile test of the steel rope, toextract material parameters such as an elastic modulus E, a yieldstrength σ_(y), an ultimate strength σ_(b), a maximum plastic strainε^(p), etc.; a tension-displacement curve of a ring chain is obtainedthrough the breaking test of the three-ring ring chain, to extract aninitial length l_(N0) of the ring chain, a length l_(N1) at a bentboundary moment, a tension F_(N1), an axial stress σ_(N1), a developmentdegree of the axial stress γ_(N1), a length l_(N2) at a breaking moment,a tension F_(N2), an axial stress σ_(N2), and a development degree ofthe axial stress γ_(N2); the critical damage criterion when puncturingoccurs in the ring net panel is obtained, wherein, the critical damagecriterion is that the development degree of a maximum axial stress ofthe net ring in a force transmission path of the edge of the loadedregion of the ring net panel is:$\gamma_{N\max} = {\gamma_{N2} = {\frac{\sigma_{N2}}{\sigma_{y}} = {\frac{F_{N2}}{( {2\sigma_{y}A} )}.}}}$12. The method according to claim 2, wherein the steel rope having highstrength in the step (1) is a basic material of manufacturing the ringnet panel, a surface of the steel rope is plated with anti-corrosioncoating, and a diameter d_(min) of the steel rope is 2 mm-3 mm; thesteel rope having high strength is formed to a single steel rope netring having the inner diameter of d after winding a mold a certainnumber of turns, and the net ring is a basic unit of the ring net panel;the ring net panel is formed by nesting the plurality of single rings ina four-nested-into-one mode, and an external contour of the ring netpanel is rectangular.
 13. The method according to claim 3, wherein thesteel rope having high strength in the step (1) is a basic material ofmanufacturing the ring net panel, a surface of the steel rope is platedwith anti-corrosion coating, and a diameter d_(min) of the steel rope is2 mm-3 mm; the steel rope having high strength is formed to a singlesteel rope net ring having the inner diameter of d after winding a molda certain number of turns, and the net ring is a basic unit of the ringnet panel; the ring net panel is formed by nesting the plurality ofsingle rings in a four-nested-into-one mode, and an external contour ofthe ring net panel is rectangular.
 14. The method according to claim 4,wherein the steel rope having high strength in the step (1) is a basicmaterial of manufacturing the ring net panel, a surface of the steelrope is plated with anti-corrosion coating, and a diameter d_(min) ofthe steel rope is 2 mm-3 mm; the steel rope having high strength isformed to a single steel rope net ring having the inner diameter of dafter winding a mold a certain number of turns, and the net ring is abasic unit of the ring net panel; the ring net panel is formed bynesting the plurality of single rings in a four-nested-into-one mode,and an external contour of the ring net panel is rectangular.
 15. Themethod according to claim 5, wherein the steel rope having high strengthin the step (1) is a basic material of manufacturing the ring net panel,a surface of the steel rope is plated with anti-corrosion coating, and adiameter d_(min) of the steel rope is 2 mm-3 mm; the steel rope havinghigh strength is formed to a single steel rope net ring having the innerdiameter of d after winding a mold a certain number of turns, and thenet ring is a basic unit of the ring net panel; the ring net panel isformed by nesting the plurality of single rings in afour-nested-into-one mode, and an external contour of the ring net panelis rectangular.
 16. The method according to claim 6, wherein the steelrope having high strength in the step (1) is a basic material ofmanufacturing the ring net panel, a surface of the steel rope is platedwith anti-corrosion coating, and a diameter d_(min) of the steel rope is2 mm-3 mm; the steel rope having high strength is formed to a singlesteel rope net ring having the inner diameter of d after winding a molda certain number of turns, and the net ring is a basic unit of the ringnet panel; the ring net panel is formed by nesting the plurality ofsingle rings in a four-nested-into-one mode, and an external contour ofthe ring net panel is rectangular.
 17. The method according to claim 7,wherein the steel rope having high strength in the step (1) is a basicmaterial of manufacturing the ring net panel, a surface of the steelrope is plated with anti-corrosion coating, and a diameter d_(min) ofthe steel rope is 2 mm-3 mm; the steel rope having high strength isformed to a single steel rope net ring having the inner diameter of dafter winding a mold a certain number of turns, and the net ring is abasic unit of the ring net panel; the ring net panel is formed bynesting the plurality of single rings in a four-nested-into-one mode,and an external contour of the ring net panel is rectangular.
 18. Themethod according to claim 8, wherein the steel rope having high strengthin the step (1) is a basic material of manufacturing the ring net panel,a surface of the steel rope is plated with anti-corrosion coating, and adiameter d_(min) of the steel rope is 2 mm-3 mm; the steel rope havinghigh strength is formed to a single steel rope net ring having the innerdiameter of d after winding a mold a certain number of turns, and thenet ring is a basic unit of the ring net panel; the ring net panel isformed by nesting the plurality of single rings in afour-nested-into-one mode, and an external contour of the ring net panelis rectangular.
 19. The method according to claim 9, wherein the steelrope having high strength in the step (1) is a basic material ofmanufacturing the ring net panel, a surface of the steel rope is platedwith anti-corrosion coating, and a diameter d_(min) of the steel rope is2 mm-3 mm; the steel rope having high strength is formed to a singlesteel rope net ring having the inner diameter of d after winding a molda certain number of turns, and the net ring is a basic unit of the ringnet panel; the ring net panel is formed by nesting the plurality ofsingle rings in a four-nested-into-one mode, and an external contour ofthe ring net panel is rectangular.